Question: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 6x + 4$ and $ KL = 7x - 2$ Find $JL$.
Solution: A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {6x + 4} = {7x - 2}$ Solve for $x$ $ -x = -6$ $ x = 6$ Substitute $6$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 6({6}) + 4$ $ KL = 7({6}) - 2$ $ JK = 36 + 4$ $ KL = 42 - 2$ $ JK = 40$ $ KL = 40$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {40} + {40}$ $ JL = 80$